Study of $B^0_s - \overline{B^0_s}$ oscillations and $B^0_s$ lifetimes using hadronic decays of $B^0_s$ mesons

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− B

using hadronic decays of B0_{_s mesons}

P. Abreu, W. Adam, T. Adye, P. Adzic, I. Azhinenko, Z. Albrecht, T. Alderweireld, G.D. Alekseev, R. Alemany, T. Allmendinger, et al.

To cite this version:

P. Abreu, W. Adam, T. Adye, P. Adzic, I. Azhinenko, et al.. Study of B0_{_s− B}0_{_s oscillations and}

B0_s lifetimes using hadronic decays of B0_{_s mesons. European Physical Journal C: Particles and}

CERN{EP/2000-087 28March2000

Study of

oscillations

and

lifetimes using

hadronic decays of

mesons

Abstract

Oscillations of B0_{s mesons have been studied in samples selected from about 3.5}

million hadronic Z decays detected by DELPHI between 1992 and 1995. One

analysis uses events in the exclusive decay channels: B0s !D

,

s+ or D,

sa+1 and

B_0s !D

0_K,+ or D0K,a+1, where the D decays are completely reconstructed.

In addition, B0_s

,B

0

s oscillations have been studied in events with an exclusively

reconstructed Ds accompanied in the same hemisphere by a high momentum

hadron of opposite charge. Combining the two analyses, a limit on the mass

dierence between the physical B0_{s states has been obtained:}

mB0 s > 4:0 ps ,1 at the 95% C.L. with a sensitivity of
mB0 s = 3:2 ps ,1:

Using the latter sample of events, the B0s lifetime has been measured and an

upper limit on the decay width dierence between the two physical B0s states

has been obtained:

B0 s = 1:53 +0:16 ,0:15(stat:) 0:07(syst:) ps
,B0 s=,B 0 s < 0:69 at the 95% C.L.

The combination of these results with those obtained using D

P.Abreu , W.Adam , T.Adye , P.Adzic , I.Ajinenko , Z.Albrecht , T.Alderweireld , G.D.Alekseev , R.Alemany50, T.Allmendinger18, P.P.Allport23, S.Almehed25, U.Amaldi9, N.Amapane46, S.Amato48, E.G.Anassontzis3,

P.Andersson45, A.Andreazza9, S.Andringa22, P.Antilogus26, W-D.Apel18, Y.Arnoud9, B.Asman45, J-E.Augustin26,

A.Augustinus9, P.Baillon9, P.Bambade20, F.Barao22, G.Barbiellini47, R.Barbier26, D.Y.Bardin17, G.Barker18,

A.Baroncelli39, M.Battaglia16, M.Baubillier24, K-H.Becks53, M.Begalli6, A.Behrmann53, P.Beilliere8, Yu.Belokopytov9,

N.C.Benekos32, A.C.Benvenuti5, C.Berat15, M.Berggren26, D.Bertini26, D.Bertrand2, M.Besancon40, M.Bigi46,

M.S.Bilenky17, M-A.Bizouard20, D.Bloch10, H.M.Blom31, M.Bonesini28, W.Bonivento28, M.Boonekamp40,

P.S.L.Booth23, A.W.Borgland4, G.Borisov20, C.Bosio42, O.Botner49, E.Boudinov31, B.Bouquet20, C.Bourdarios20,

T.J.V.Bowcock23, I.Boyko17, I.Bozovic12, M.Bozzo14, M.Bracko44, P.Branchini39, T.Brenke53, R.A.Brenner49,

P.Bruckman9, J-M.Brunet8, L.Bugge33, T.Buran33, T.Burgsmueller53, B.Buschbeck51, P.Buschmann53, S.Cabrera50,

M.Caccia28, M.Calvi28, T.Camporesi9, V.Canale38, F.Carena9, L.Carroll23, C.Caso14, M.V.Castillo Gimenez50,

A.Cattai9, F.R.Cavallo5, V.Chabaud9, Ph.Charpentier9, L.Chaussard26, P.Checchia36, G.A.Chelkov17, R.Chierici46,

P.Chliapnikov43, P.Chochula7, V.Chorowicz26, J.Chudoba30, K.Cieslik19, P.Collins9, R.Contri14, E.Cortina50,

G.Cosme20, F.Cossutti9, H.B.Crawley1, D.Crennell37, S.Crepe15, G.Crosetti14, J.Cuevas Maestro34, S.Czellar16,

M.Davenport9, W.Da Silva24, A.Deghorain2, G.Della Ricca47, P.Delpierre27, N.Demaria9, A.De Angelis9, W.De Boer18,

C.De Clercq2, B.De Lotto47, A.De Min36, L.De Paula48, H.Dijkstra9, L.Di Ciaccio38;9, J.Dolbeau8, K.Doroba52,

M.Dracos10, J.Drees53, M.Dris32, A.Duperrin26, J-D.Durand9, G.Eigen4, T.Ekelof49, G.Ekspong45, M.Ellert49,

M.Elsing9, J-P.Engel10, M.Espirito Santo22, G.Fanourakis12, D.Fassouliotis12, J.Fayot24, M.Feindt18, A.Fenyuk43,

P.Ferrari28, A.Ferrer50, E.Ferrer-Ribas20, F.Ferro14, S.Fichet24, A.Firestone1, U.Flagmeyer53, H.Foeth9, E.Fokitis32,

F.Fontanelli14, B.Franek37, A.G.Frodesen4, R.Fruhwirth51, F.Fulda-Quenzer20, J.Fuster50, A.Galloni23, D.Gamba46,

S.Gamblin20, M.Gandelman48, C.Garcia50, C.Gaspar9, M.Gaspar48, U.Gasparini36, Ph.Gavillet9, E.N.Gazis32, D.Gele10,

N.Ghodbane26, I.Gil50, F.Glege53, R.Gokieli9;52, B.Golob44, G.Gomez-Ceballos41, P.Goncalves22,

I.Gonzalez Caballero41, G.Gopal37, L.Gorn1;54, Yu.Gouz43, V.Gracco14, J.Grahl1, E.Graziani39, H-J.Grimm18, P.Gris40,

G.Grosdidier20, K.Grzelak52, M.Gunther49, J.Guy37, F.Hahn9, S.Hahn53, S.Haider9, A.Hallgren49, K.Hamacher53,

J.Hansen33, F.J.Harris35, V.Hedberg25, S.Heising18, J.J.Hernandez50, P.Herquet2, H.Herr9, T.L.Hessing35,

J.-M.Heuser53, E.Higon50, S-O.Holmgren45, P.J.Holt35, S.Hoorelbeke2, M.Houlden23, J.Hrubec51, K.Huet2,

G.J.Hughes23, K.Hultqvist45, J.N.Jackson23, R.Jacobsson9, P.Jalocha19, R.Janik7, Ch.Jarlskog25, G.Jarlskog25,

P.Jarry40, B.Jean-Marie20, D.Jeans35, E.K.Johansson45, P.Jonsson26, C.Joram9, P.Juillot10, F.Kapusta24,

K.Karafasoulis12, S.Katsanevas26, E.C.Katsous32, R.Keranen18, G.Kernel44, B.P.Kersevan44, B.A.Khomenko17,

N.N.Khovanski17, A.Kiiskinen16, B.King23, A.Kinvig23, N.J.Kjaer31, O.Klapp53, H.Klein9, P.Kluit31, P.Kokkinias12,

M.Koratzinos9, V.Kostioukhine43, C.Kourkoumelis3, O.Kouznetsov40, M.Krammer51, E.Kriznic44, Z.Krumstein17,

P.Kubinec7, J.Kurowska52, K.Kurvinen16, J.W.Lamsa1, D.W.Lane1, P.Langefeld53, V.Lapin43, J-P.Laugier40,

R.Lauhakangas16, G.Leder51, F.Ledroit15, V.Lefebure2, L.Leinonen45, A.Leisos12, R.Leitner30, J.Lemonne2, G.Lenzen53,

V.Lepeltier20, T.Lesiak19, M.Lethuillier40, J.Libby35, D.Liko9, A.Lipniacka45, I.Lippi36, B.Loerstad25, J.G.Loken35,

J.H.Lopes48, J.M.Lopez41, R.Lopez-Fernandez15, D.Loukas12, P.Lutz40, L.Lyons35, J.MacNaughton51, J.R.Mahon6,

A.Maio22, A.Malek53, T.G.M.Malmgren45, S.Maltezos32, V.Malychev17, F.Mandl51, J.Marco41, R.Marco41,

B.Marechal48, M.Margoni36, J-C.Marin9, C.Mariotti9, A.Markou12, C.Martinez-Rivero20, F.Martinez-Vidal50,

S.Marti i Garcia9, J.Masik13, N.Mastroyiannopoulos12, F.Matorras41, C.Matteuzzi28, G.Matthiae38, F.Mazzucato36,

M.Mazzucato36, M.Mc Cubbin23, R.Mc Kay1, R.Mc Nulty23, G.Mc Pherson23, C.Meroni28, W.T.Meyer1, A.Miagkov43,

E.Migliore9, L.Mirabito26, W.A.Mitaro51, U.Mjoernmark25, T.Moa45, M.Moch18, R.Moeller29, K.Moenig9;11,

M.R.Monge14, X.Moreau24, P.Morettini14, G.Morton35, U.Mueller53, K.Muenich53, M.Mulders31, C.Mulet-Marquis15,

R.Muresan25, W.J.Murray37, B.Muryn15;19, G.Myatt35, T.Myklebust33, F.Naraghi15, M.Nassiakou12, F.L.Navarria5,

S.Navas50, K.Nawrocki52, P.Negri28, N.Neufeld9, R.Nicolaidou40, B.S.Nielsen29, P.Niezurawski52, M.Nikolenko10;17,

V.Nomokonov16, A.Nygren25, V.Obraztsov43, A.G.Olshevski17, A.Onofre22, R.Orava16, G.Orazi10, K.Osterberg16,

A.Ouraou40, M.Paganoni28, S.Paiano5, R.Pain24, R.Paiva22, J.Palacios35, H.Palka19, Th.D.Papadopoulou32;9,

K.Papageorgiou12, L.Pape9, C.Parkes9, F.Parodi14, U.Parzefall23, A.Passeri39, O.Passon53, T.Pavel25, M.Pegoraro36,

L.Peralta22, M.Pernicka51, A.Perrotta5, C.Petridou47, A.Petrolini14, H.T.Phillips37, F.Pierre40, M.Pimenta22,

E.Piotto28, T.Podobnik44, M.E.Pol6, G.Polok19, P.Poropat47, V.Pozdniakov17, P.Privitera38, N.Pukhaeva17, A.Pullia28,

D.Radojicic35, S.Ragazzi28, H.Rahmani32, J.Rames13, P.N.Rato21, A.L.Read33, P.Rebecchi9, N.G.Redaelli28,

M.Regler51, D.Reid31, R.Reinhardt53, P.B.Renton35, L.K.Resvanis3, F.Richard20, J.Ridky13, G.Rinaudo46, O.Rohne33,

A.Romero46, P.Ronchese36, E.I.Rosenberg1, P.Rosinsky7, P.Roudeau20, T.Rovelli5, Ch.Royon40, V.Ruhlmann-Kleider40,

A.Ruiz41, H.Saarikko16, Y.Sacquin40, A.Sadovsky17, G.Sajot15, J.Salt50, D.Sampsonidis12, M.Sannino14, H.Schneider18,

Ph.Schwemling24, B.Schwering53, U.Schwickerath18, F.Scuri47, P.Seager21, Y.Sedykh17, A.M.Segar35, R.Sekulin37,

R.C.Shellard6, M.Siebel53, L.Simard40, F.Simonetto36, A.N.Sisakian17, G.Smadja26, N.Smirnov43, O.Smirnova25,

G.R.Smith37, A.Sokolov43, A.Sopczak18, R.Sosnowski52, T.Spassov22, E.Spiriti39, P.Sponholz53, S.Squarcia14,

C.Stanescu39, S.Stanic44, K.Stevenson35, A.Stocchi20, J.Strauss51, R.Strub10, B.Stugu4, M.Szczekowski52,

M.Szeptycka52, T.Tabarelli28, A.Taard23, F.Tegenfeldt49, F.Terranova28, J.Thomas35, J.Timmermans31, N.Tinti5,

P.Van Dam31, W.Van Den Boeck2, W.K.Van Doninck2, J.Van Eldik31, A.Van Lysebetten2, N.Van Remortel2,

I.Van Vulpen31, G.Vegni28, L.Ventura36, W.Venus37;9, F.Verbeure2, M.Verlato36, L.S.Vertogradov17, V.Verzi38,

D.Vilanova40, L.Vitale47, E.Vlasov43, A.S.Vodopyanov17, C.Vollmer18, G.Voulgaris3, V.Vrba13, H.Wahlen53, C.Walck45,

A.J.Washbrook23, C.Weiser18, D.Wicke53, J.H.Wickens2, G.R.Wilkinson9, M.Winter10, M.Witek19, G.Wolf9, J.Yi1,

O.Yushchenko43, A.Zalewska19, P.Zalewski52, D.Zavrtanik44, E.Zevgolatakos12, N.I.Zimin17;25, A.Zintchenko17,

G.C.Zucchelli45, G.Zumerle36

1Department of Physics and Astronomy, Iowa State University, Ames IA 50011-3160, USA 2Physics Department, Univ. Instelling Antwerpen, Universiteitsplein 1, BE-2610 Wilrijk, Belgium

and IIHE, ULB-VUB, Pleinlaan 2, BE-1050 Brussels, Belgium

and Faculte des Sciences, Univ. de l'Etat Mons, Av. Maistriau 19, BE-7000 Mons, Belgium

3Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece 4Department of Physics, University of Bergen, Allegaten 55, NO-5007 Bergen, Norway

5Dipartimento di Fisica, Universita di Bologna and INFN, Via Irnerio 46, IT-40126 Bologna, Italy 6Centro Brasileiro de Pesquisas Fsicas, rua Xavier Sigaud 150, BR-22290 Rio de Janeiro, Brazil

and Depto. de Fsica, Pont. Univ. Catolica, C.P. 38071 BR-22453 Rio de Janeiro, Brazil

and Inst. de Fsica, Univ. Estadual do Rio de Janeiro, rua S~ao Francisco Xavier 524, Rio de Janeiro, Brazil

7Comenius University, Faculty of Mathematics and Physics, Mlynska Dolina, SK-84215 Bratislava, Slovakia 8College de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, FR-75231 Paris Cedex 05, France 9CERN, CH-1211 Geneva 23, Switzerland

10Institut de Recherches Subatomiques, IN2P3 - CNRS/ULP - BP20, FR-67037 Strasbourg Cedex, France 11DESY-Zeuthen, Platanenallee 6, D-15735 Zeuthen, Germany

12Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece

13FZU, Inst. of Phys. of the C.A.S. High Energy Physics Division, Na Slovance 2, CZ-180 40, Praha 8, Czech Republic 14Dipartimento di Fisica, Universita di Genova and INFN, Via Dodecaneso 33, IT-16146 Genova, Italy

15Institut des Sciences Nucleaires, IN2P3-CNRS, Universite de Grenoble 1, FR-38026 Grenoble Cedex, France 16Helsinki Institute of Physics, HIP, P.O. Box 9, FI-00014 Helsinki, Finland

17Joint Institute for Nuclear Research, Dubna, Head Post Oce, P.O. Box 79, RU-101 000 Moscow, Russian Federation 18Institut fur Experimentelle Kernphysik, Universitat Karlsruhe, Postfach 6980, DE-76128 Karlsruhe, Germany 19Institute of Nuclear Physics and University of Mining and Metalurgy, Ul. Kawiory 26a, PL-30055 Krakow, Poland 20Universite de Paris-Sud, Lab. de l'Accelerateur Lineaire, IN2P3-CNRS, B^at. 200, FR-91405 Orsay Cedex, France 21School of Physics and Chemistry, University of Lancaster, Lancaster LA1 4YB, UK

22LIP, IST, FCUL - Av. Elias Garcia, 14-1o, PT-1000 Lisboa Codex, Portugal

23Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK

24LPNHE, IN2P3-CNRS, Univ. Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, FR-75252 Paris Cedex 05, France 25Department of Physics, University of Lund, Solvegatan 14, SE-223 63 Lund, Sweden

26Universite Claude Bernard de Lyon, IPNL, IN2P3-CNRS, FR-69622 Villeurbanne Cedex, France 27Univ. d'Aix - Marseille II - CPP, IN2P3-CNRS, FR-13288 Marseille Cedex 09, France

28Dipartimento di Fisica, Universita di Milano and INFN, Via Celoria 16, IT-20133 Milan, Italy 29Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen , Denmark

30NC, Nuclear Centre of MFF, Charles University, Areal MFF, V Holesovickach 2, CZ-180 00, Praha 8, Czech Republic 31NIKHEF, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands

32National Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greece 33Physics Department, University of Oslo, Blindern, NO-1000 Oslo 3, Norway

34Dpto. Fisica, Univ. Oviedo, Avda. Calvo Sotelo s/n, ES-33007 Oviedo, Spain 35Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK

36Dipartimento di Fisica, Universita di Padova and INFN, Via Marzolo 8, IT-35131 Padua, Italy 37Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK

38Dipartimento di Fisica, Universita di Roma II and INFN, Tor Vergata, IT-00173 Rome, Italy

39Dipartimento di Fisica, Universita di Roma III and INFN, Via della Vasca Navale 84, IT-00146 Rome, Italy 40DAPNIA/Service de Physique des Particules, CEA-Saclay, FR-91191 Gif-sur-Yvette Cedex, France 41Instituto de Fisica de Cantabria (CSIC-UC), Avda. los Castros s/n, ES-39006 Santander, Spain

42Dipartimento di Fisica, Universita degli Studi di Roma La Sapienza, Piazzale Aldo Moro 2, IT-00185 Rome, Italy 43Inst. for High Energy Physics, Serpukov P.O. Box 35, Protvino, (Moscow Region), Russian Federation

44J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia and Laboratory for Astroparticle Physics,

Nova Gorica Polytechnic, Kostanjeviska 16a, SI-5000 Nova Gorica, Slovenia, and Department of Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia

45Fysikum, Stockholm University, Box 6730, SE-113 85 Stockholm, Sweden

46Dipartimento di Fisica Sperimentale, Universita di Torino and INFN, Via P. Giuria 1, IT-10125 Turin, Italy 47Dipartimento di Fisica, Universita di Trieste and INFN, Via A. Valerio 2, IT-34127 Trieste, Italy

and Istituto di Fisica, Universita di Udine, IT-33100 Udine, Italy

48Univ. Federal do Rio de Janeiro, C.P. 68528 Cidade Univ., Ilha do Fund~ao BR-21945-970 Rio de Janeiro, Brazil 49Department of Radiation Sciences, University of Uppsala, P.O. Box 535, SE-751 21 Uppsala, Sweden

50IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, ES-46100 Burjassot (Valencia), Spain 51Institut fur Hochenergiephysik, Osterr. Akad. d. Wissensch., Nikolsdorfergasse 18, AT-1050 Vienna, Austria 52Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland

1 Introduction

In this paper, the average lifetimeof the B0smeson is measured and limitsare derived on

the oscillation frequency of the B0s-B0s system,
mB0

s, and on the decay width dierence,

,B0

s, between mass eigenstates of this system.

Starting with a B_0smeson produced at timet=0, the probability,P(t), to observe a B0s

or a B0s decaying at the proper timet can be written, neglecting eects from CP violation:

P(t) = , B0 s 2 e,, B 0 s t_(cosh(
,B0 s 2 t)  cos(
mB0 st)) (1) where ,B0 s = (,HB 0 s + ,LB 0 s)=2,
,B 0 s = ,LB 0 s ,,HB 0 s and
mB 0 s = mHB 0 s , mLB 0 s; L and

H denote the light and heavy physical states, respectively;
,B0

s and
mB

0

s are dened

to be positive [1] and the plus (minus) signs in equation (1) refer to B0s (B0s) decays.

The oscillation period gives a direct measurement of the mass dierence between the

two physical states. The Standard Model predicts that
,B0

s


mB0

s and the previous

expression simplies to : P unmix B0 s (t) = ,B 0 s e ,, B 0 s t_cos2_(
mB0 st 2 ) (2)

for B0s!B0s and similarly:

P mix B0 s (t) = ,B 0 s e ,, B 0 s t_sin2_(
mB0 st 2 ) (3)

for B0s ! B0s. The oscillation frequency, proportional to
mB

0

s, can be obtained from

the t of the time distributions given in relations (2) and (3), whereas expression (1),

without distinguishing between the B0s and the B0s, can be used to determine the average

lifetime and the dierence between the lifetimes of the heavy and light mass eigenstates1_.

B physics allows a precise determination of some of the parameters of the CKM matrix. All the nine elements can be expressed in term of 4 parameters that are, in Wolfenstein

parameterisation [2], , A,  and . The most uncertain parameters are  and .

Several quantities which depend on  and  can be measured and, if the Standard

Model is correct, they must dene compatible values for the two parameters inside

mea-surement errors and theoretical uncertainties. These quantities are K, the parameter

introduced to measure CP violation in the K system, jVubj=jVcbj, the ratio between the

modulus of the CKM matrix elements corresponding to b!u and b!c transitions, and

the mass dierence
mB0

d.

In the Standard Model, B0q-B0q (q = d;s) mixing is a direct consequence of second

order weak interactions. Having kept only the dominant top quark contribution,
mB0

q

can be expressed in terms of Standard Model parameters [3]:

mB0 q= G 2F 62jVtbj 2 jVtqj 2_m2tmB qf2B qBB qBF(xt): (4)

In this expression GF is the Fermi coupling constant; F(xt), with xt = m2

t

m2 W

, results from the evaluation of the second order weak \box" diagram responsible for the mixing and has

a smooth dependence on xt; B is a QCD correction factor obtained at next-to-leading

1Throughout the paper the dimension of
m B

0 s

will be expressed in ps,1units, because the argument
m B

0 st in the

expression (1) has no dimension. The conversion is given by ps,1= 6:58 10

order in perturbative QCD [4]. The dominant uncertainties in equation (4) come from

the evaluation of the B meson decay constantfBq and of the \bag" parameterBBq. The

two elements of the VCKM matrix are equal to:

jVtdj=A

3q

(1,)2+2 ; jVtsj=A

2_{; (5)}

neglecting terms of order O(4).

In the Wolfenstein parameterisation, jVtsj is independent of  and . A measurement

of
mB0

s is thus a way to measure the value of the non-perturbative QCD parameters.

Direct information on Vtd can be inferred by measuring
mB0

d. Several experiments

have accurately measured
mB0

d, nevertheless this precision cannot be fully exploited to

extract information on  and  because of the large uncertainty which originates in the

evaluation of the non-perturbative QCD parameters.

An ecient constraint is the ratio between the Standard Model expectations for
mB0

d and
mB0 s, given by:
mB0 d
mB0 s = mB0 df 2 B0 d BB0 dB 0 d mB0 sf2B 0 sBB 0 sB 0 s jVtdj 2 jVtsj 2 : (6)

A measurement of the ratio
mB0

d=
mB 0

s gives the same type of constraint, in the 

,

plane, as a measurement of
mB0

d, but is expected to be better under control from theory,

since the ratios of the decay constants fBq and of the bag parameters BBq for B0d and B0s

are better known than their individual values [5].

Using existing measurements which constrain  and , except those on
mB0

s, the

distribution for the expected values of
mB0

s can be obtained. It has been shown, for

example, in the context of the Electroweak Standard Model and QCD assumptions, that

mB0

s has to lie, at 68% C.L., between 8 ps

,1 and 16 ps,1 and is expected to be smaller

than 21 ps,1 at the 95% C.L. [6].

The search for B0s , B0s oscillations has been the subject of recent intense

activi-ty. No signal has been observed so far and the lower limit on the oscillation frequency comes from the combination of the results obtained at LEP, CDF and SLD experiments:

mB0

s > 14:3 ps

,1 at the 95% C.L. [7]. The sensitivity of present measurements is

es-timated as 14:7 ps,1. These results have been obtained by combining analyses which

select various B0s decay channels2_{. Some analyses [8,9] use events containing simply a}

lepton emitted at large transverse momentum relative to the axis of the jet from which it emerges. In this case, the proper time is measured using an inclusive vertex algorithm to reconstruct the decay distance and the energy of the B hadron candidate. In other

analyses, like D

s `[10,11], the identied lepton is accompanied, in the same hemisphere,

by an exclusively reconstructed Ds. In D

s h analyses (see [12] and the present paper),

such leptons are replaced by one or more charged hadrons.

Progress before the next generation accelerators is expected to come from improved analyses of these channels, but the sensitivity at high frequency is essentially limited by the damping of the reconstructed oscillation amplitude due to the limited resolution on

the B0s proper time. In general, the proper time resolutiontcontains two terms and one

of them is a time-dependent:

t=

q

L2+ (p=p)2 t2 (7)

where L is related to the decay distance resolution, p=p is the relative error on the

momentum reconstruction and t is the proper decay time. The damping factor of the

oscillation amplitude in this case is given by the following expression [13]:

damping = exp(,(
mB 0 sL) 2₌₂₎p )(x)exp(x2_{)ERFC(x); (8)} where x=1/p 2/
mB0 s 1/(p/p) and ERFC(x)=2= p  R 1 x e,t 2 dt.

Exclusive (completelyreconstructed) decays have a better time resolution for two reasons.

As there is no missing particle in the decay, the B0s momentum is known with a good

precision and therefore the contribution of the momentum uncertainty to the proper

time resolution is negligible. Hence, t = L and the previous expression is simplied:

damping = exp(,(
mB0

sL)

2_{=2). In addition, the reconstructed channels are two-body}

or quasi two-body decays, with an opening angle of their decay products which is on average larger than in multi-body nal states; this results in a better accuracy on their decay position determination.

The B0smeson lifetimeis expected to be equal to the B0dlifetime[14] within one percent.

In the Standard Model, the ratio between the decay width and the mass dierences in the

B0_-B0 _{system is of the order of (mb=mt)}2_{, although large QCD corrections are expected.}

Explicitcalculations to leading order in QCD correction, in the OPE formalism[1] predict:

,B0 s=,B 0 s = 0:16 +0:11 ,0:09

where the quoted error is dominated by the uncertainty related to hadronic matrix ele-ments. Recent calculations [15] at next-to-leading order predict a lower value:

,B0 s=,B 0 s = 0:006 +0:150 ,0:063 :

An interesting approach consists in using the ratio between
,B0

s and
mB 0 s [15]:
,B0 s
mB0 s = (2:63+0:67 ,1:36)10 ,3 ; (9)

to constrain the upper part of the
mB0

s spectrum with an upper limit on
,B

0 s=,B

0

s. If,

in future, the theoretical uncertainty can be reduced, this method can give an alternative

way of determining
mB0

s via
,B

0

s and, in conjunction with the determination of
mB

0 d,

can provide an extra constraint on the  and  parameters.

After a description of the main features of the DELPHI detector, the event selection

and the event simulation in Section 2, the two B0s analyses are described. Section 3

presents an analysis of B0s-B0s oscillations from a sample of 44 exclusively reconstructed

B0s decays. Section 4 is dedicated to the D

sh analysis, in which B

0s ! DshX decays

with fully reconstructed Ds are selected. This analysis also includes a measurement of

the B0s meson lifetime and sets a limit on the dierence between the decay widths of

the physical B0s states,
,B0

s=,B 0

s. In Section 5 the combined limit on
mB

0

s is given.

Finally in Section 6, these three results are combined with those obtained using a D

s `

sample [10].

2 The DELPHI detector

2.1 Charged particle reconstruction

The detector elements used for tracking are the Vertex Detector (VD), the Inner Detector (ID), the Time Projection Chamber (TPC) and the Outer Detector (OD). The VD provides the high precision needed near the primary vertex.

For the data taken from 1991 to 1993, the VD consisted of three cylindrical layers of silicon detectors (at radii of 6.3, 9.0 and 10.9 cm) measuring points in the plane transverse

to the beam direction (r coordinate3_{) in the polar angle range between 43} and 137.

In 1994, the rst and the third layers were equipped with detector modules with double

sided readout, providing a single hit precision of 7.6 m in r, similar to that obtained

previously, and 9 m in z [17]. For high momentum particles with associated hits in the

VD, the impact parameter precision close to the interaction region is 20 m in the r

plane and 34 m in the rz plane. Charged particle tracks are reconstructed with 95%

eciency and with a momentum resolutionp=p < 1:510

,3p (p in GeV=c) in the polar

angle region between 25 and 155.

2.2 Hadronic Z selection and event topology

Hadronic events from Z decays were selected by requiring a multiplicity of charged

particles greater than four and a total energy of charged particles greater than 0.12p

s,

wherep

s is the centre-of-mass energy and all particles were assumed to be pions; charged

particles were required to have a momentum greater than 0.4 GeV=c and a polar angle

between 20 and 160. The overall trigger and selection eciency is (95.0

0.1)% [18]. A

total of 3.5 million hadronic events was obtained from the 1992-1995 data.

Each selected event was divided into two hemispheresseparated by the plane transverse to the sphericity axis. A clustering analysis, based on the JETSET algorithm LUCLUS with default parameters [19], was used to dene jets using both charged and neutral

particles. These jets were used to compute the pout_{t of each particle of the event, as the}

transverse momentum of this particle with respect to the axis of the jet it belonged to, after having removed this particle from its jet.

2.3 Hadron identication

Hadron identication relied on the RICH detector and on the specic ionisation mea-surement performed by the TPC.

The RICH detector [16] used two radiators. A gas radiator separated kaons from

pions between 3 and 9 GeV=c, where kaons gave no Cherenkov light whereas pions did,

and between 9 and 16 GeV=c, using the measured Cherenkov angle. It also provided

kaon/proton separation from 8 to 20 GeV=c. A liquid radiator, which has been fully

operational since 1994, provided p=K= separation in the momentum range between 0.7 and 8 GeV=c.

The specic energy loss per unit length (dE=dx) was measured in the TPC by using up to 192 sense wires. At least 30 contributing measurements were required to compute the truncated mean. In the momentum range between 3 and 25 GeV=c, this is fullled

for 55% of the tracks and the dE=dx measurement has a precision of 7%.

The combination of the two measurements, dE=dx and RICH, provides four levels

of pion, kaon and proton tagging [20]: \very loose", \loose", \standard" and \tight" corresponding to dierent purities. The eciency and purity of the tagging depend on

3The DELPHI reference frame is dened with z along the e, beam, x towards the centre of LEP and y upwards.

the momentum of the particle. In the typical momentum range of the B decay products between 2 and 10 GeV=c, the average eciency (purity) is about 75% (50%) for the \loose", 65% (60%), for the \standard" and 55% (70%) for the \tight" kaon tag. The \very loose" tag indicates that the particle is not identied as a pion. The purity is the proportion of genuine kaons in the selected sample.

Very recently a neural network algorithm has been developed in order to combine the dierent RICH identication packages optimally. The result of the neural network gives

a tagging variable xnet, which varies from,1 (pure background) to +1 (pure signal). In

order to use the same denitions of the kaon tag through all the paper, the \very loose",

\loose", \standard" and \tight" tags were dened for a tagging variable xnet larger than

,0:2, 0:0, 0:4 and 0:6, respectively. This second algorithm has been used in the D



s h

analysis (Section 4).

2.4 Primary and B vertices reconstruction

The average beam spot position evaluated using the events from dierent periods of

data taking has been used as a constraint in the determination of the e+_e, interaction

point on an event-by-event basis [16]. In 1994 and 1995 data, the position of the primary

vertex transverse to the beam is determined with a precision of about 40 m in the

horizontal direction, and about 10 m in the vertical direction. For 1992 and 1993 data,

the uncertainties are larger by about 50%.

For both 1992-1993 and 1994-1995 data, the B decay length was estimated as L =

Lxy=sinB, where Lxy is the measured distance between the primary vertex and the B

decay vertex in the plane transverse to the beam direction and B is the polar angle of

the B ight direction, estimated from the B decay products. The transverse decay length

Lxy was given the same sign as the scalar product of the B momentum with the vector

joining the primary to the secondary vertex; this procedure gives signed decay length L.

2.5

and

reconstruction

, decays have been reconstructed using a kinematic t.

The distance in the r plane between the V0 _{decay point and the primary vertex was}

required to be less than 90 cm. This condition meant that the decay products had track

segments of at least 20 cm long in the TPC. The reconstruction of the V0 _{vertex and}

selection cuts are described in detail in reference [16]. Only K0s candidates passing the

\tight" selection criteria dened in [16] were retained for this analysis.

2.6 b-tagging

The b-tagging package is described in reference [21]. The impact parameters of the charged particle tracks, with respect to the primary vertex, were used to build the prob-ability that all tracks come from this vertex. Due to the long B hadron lifetimes, the probability distribution is peaked near zero for events which contain beauty quark where-as it is at for events containing only light quarks.

2.7 Event simulation

semileptonic decays were simulated using the ISGW model [23]. Generated events were passed through the full simulation of the DELPHI detector [16], and the resulting sim-ulated raw data were processed through the same reconstruction and analysis programs as the real data.

3 Exclusively reconstructed

decays

3.1 Evaluation of

s

branching fractions

For this analysis B0s mesons were reconstructed in D,

s +, D,

s a+1, D0K,+and D0K,a+1

decay channels. Contributions to the mass spectrum can come also from other decay

chan-nels such as D, s +, D, s a+1, D (2007)0_K,+, D  (2007)0_K,a+1, D, s + and D, s +, where

the cascade photon or the neutral pion has not been reconstructed. All correspond-ing branchcorrespond-ing fractions are unmeasured. An estimation will be used in the followcorrespond-ing to

evaluate the number of the expected B0s events.

To evaluate the two-body B_0s!D(

),

s +(a+1) branching fractions, the equivalent decay

channels for non-strange mesons were used. This evaluation is based on the numerical application of factorisation done in reference [24].

For each decay mode of the B0s !D(

),

s M+, where M+ is a + or a +, the branching

fraction is estimated using the following formula:

Br(B0_s !D (), s M+) = Brexp(B0d !D (),M+)Br th_(B0s !D( ), s M+) Brth_(B0d!D( ),M+); (10)

where the notation D(), means D(2010), or D, meson. The superscript \exp"

des-ignates the experimentally measured values [25], and \th" the predictions from refer-ence [24]. The theoretical ratios in equation (10) are close to 1.

For the two-body decays containing D mesons with a1, the theoretical branching

frac-tions are not available, and the same factors as for the + _{channels have been assumed.}

B0d decay channel Measured Br B0s decay channel Estimated Br

B0d!D ,+ (3:0 0:4)10 ,3 B0s !D , s+ (3:40:4)10 ,3 B0d!D (2010),+ (2:8 0:2)10 ,3 B0s !D , s + (3:00:2)10 ,3 B0d!D ,+ (7:9 1:4)10 ,3 B0s !D , s+ (9:01:6)10 ,3 B0d!D (2010),+ (6:7 3:3)10 ,3 B 0s !D , s + (6:93:4)10 ,3 B0d!D ,a+1 (6:0 3:3)10 ,3 B0s !D , sa+1 (6:83:6)10 ,3 B0d!D (2010),a+1 (13:0 2:7)10 ,3 B0s !D , s a+1 (13:32:8)10 ,3 B0d!D ()0 ,+ see Section 3.4 B0s !D ()0 K,+ (0:9 0:5)10 ,3 B0d!D ()0 ,a+1 see Section 3.4 B0s !D ()0 K,a+1 (3:0 1:7)10 ,3

Table 1: Values of the B0s branching fractions used in the current analysis. The notation

D()0

denes D

(2007)0 _{or D}0 _{charmed hadrons.}

Similar considerations are applied to the three-body decays B0s ! D

0_K,+(a+1) and

B0s ! D



(2007)0_K,+(a+1) using the measurements of Br(B0d

!D

0_,+) and Br(B0d

!

D0,a+1), which are described in the Section 3.4 of the current paper. The ratio of B

0s

ratio of the four previous decay modes). Finally, the factor 3.3 was used as the ratio

between the B0s decay modes containing a+1 and + _{mesons. This factor was taken as an}

average between the experimental values for the following B0d two-body decays:

Br(B_0d!D ,a+1) + Br(B0d !D (2010),a+1) Br(B0d !D ,+) + Br(B0d !D (2010),+) = 3:3 0:9 :

The theoretical calculation [26] gives for this ratio values between 3.4 and 3.5. Table 1 presents the evaluations of several branching fractions of interest for this paper.

3.2 Event Sample

Events were selected using the following decay channels:

B0s !D , s + D, s ! ,;,+,;f(980),;K 0sK,;K0K,;K0K, B0s !D , s a+1 D, s ! ,;K0K, B0s !D 0_K,+ D0 !K+ ,;K+,+, B0s !D 0_K,a+1 D0 !K+ ,;K+,+,

where the, K0s, f(980), K0, K,and a

1are reconstructed in their charged decay channels:

 ! K +_K,, K0s ! +_,, f(980) ! +_,, K0 !K +_,, K, !K0s , and a+1 !  0_+_, 0 ! + ,. D

s and D0 mesons were reconstructed by considering charged particles in

the same hemisphere with at least one VD hit.

D meson candidates were accepted if their mass was within the intervals 1:93 ,

2:01 GeV=c2 _{for Ds and 1:83},1:90 GeV=c2 for D0. The D decay length was required to

be positive and the 2_{{probability of the tted vertex to be larger than 10},5 (10,3 for

the D0 ! K decay mode). Dierent selection criteria were used for dierent decay

channels according to the optimisations derived from dedicated simulated samples. They are described in the following:

 D ,

s ! ,

The meson was reconstructed in the decay mode !K+K

,by taking all possible pairs

of oppositely charged particles if at least one of them was identied as a \very loose"

kaon. The invariant mass of these pairs had to be within 12 MeV=c

2 _{of the nominal}

 mass value [25]. The momenta of all three particles were required to be larger than

1 GeV=c. In the decay of the Ds meson into a vector () and a pseudoscalar meson (),

helicity conservation requires that the angle , measured in the vector meson rest frame

between the directions of its decay products and of the pseudoscalar meson, has a cos2

distribution. The value of jcos jwas required to be larger than 0.3.

D ,

s !

,+,

The  meson was reconstructed as in the previous channel. The momenta of all three

pions had to be larger than 0.6 GeV=c.

D ,

s !f(980)

,

The f(980) meson was reconstructed in the decay mode f(980) ! +

, by taking

al-l possibal-le pairs of oppositeal-ly charged partical-les cal-lassied as pions. This channeal-l suers from a large combinatorial background which was reduced by selecting candidates having

an invariant +_, mass within 15 MeV=c2 of the nominal f(980) mass [25] and a total

1 GeV=c.

D ,

s !K0sK ,

K0s meson reconstruction has been described in Section 2.5. In addition, the decay length

of K0s candidates had to be positive and their momentum to be larger than 2.5 GeV=c.

The momentum of the K, candidate, identied as a \very loose" kaon, had to be larger

than 1 GeV=c.

D ,

s ,!K 0K,

The K0 meson was reconstructed in the charged decay mode K0

! K

+_,. The K+

candidate was required to be identied as a \very loose" kaon. The momenta of both

particles had to be larger than 1 GeV=c and the invariant mass of the pair had to be

with-in 40 MeV=c2 of the nominal K

0 mass [25]. The value of

jcos j (see the D

,

s ! ,

selection) had to be larger than 0.3. For the K,candidate, the combinatorial background

is higher than for the kaon coming from K0 resonance. The momentum of the K,

can-didate from D,

s had to exceed 2.5 GeV=c and it had to be identied as a \loose" kaon.

D ,

s ,!K 0K,

The K0 meson was reconstructed as previously, but with an invariant mass within

60 MeV=c2 of the nominal K

0 mass [25]. This mass interval was chosen larger than

in the previous K0 selection, because of the additional constraint from the K, mass.

The K, meson was reconstructed in the decay mode K,

! K0s

,. The K0s meson

reconstruction was discussed previously. The invariant mass of K, candidates had to be

within 60 MeV=c2 of the nominal K

, mass [25]. D 0 !K +_,; D0 ! K +_,+,

The D0 meson decay to K+_, has been reconstructed by combining a kaon candidate,

identied with the \loose" tag, with an oppositely charged pion with momentum larger

than 1 GeV=c. The D0 meson decay to K+_,+, has been reconstructed by

com-bining a kaon candidate, identied with the \standard" tag, with three pions, each of

them having a momentum larger than 0.5 GeV=c. In order to reduce the combinatorial

background, for both decay modes, the kaon momentum was required to be larger than

2.5 GeV=c and the D0 momentum candidate to be larger than 10 GeV=c.

Selected D0 and D,

s mesons were used to reconstruct B0s candidates by tting a

com-mon vertex for the D,

s +, D,

sa+1, D0K,+ or D0K,a+1 systems. The  momentum had

to be larger than 4 GeV=c. The a1 candidates were reconstructed using the combination

of three pions with momenta larger than 0.8 GeV=c and with an invariant mass situated

within the interval 0:95-1:50 GeV=c2_{. At least one of the two }+_, combinations was

required to have an invariant mass lying within150 MeV=c2 of the nominal mass [25].

The a1 momentum had to be larger than 5 GeV=c (6 GeV=c for the D0 ! K

+_,++

channel). For all candidates, the D0 and D,

s meson decay distance, relative to the B

vertex had to be positive. Events with an estimated error on the B0s decay distance

larger than 250 m and those having a vertex 2_{{probability smaller than 10},3 were

removed. In order to reduce the combinatorial background from charm and light quarks, the b-tagging probability for the whole event and for the hemisphere opposite to the reconstructed B meson had to be smaller than 0.1. Additional selections which depend

combinatorial background than D, s candidates: B0s !D , s +; B0s !D , s a+1

The momentum of the B0s had to be larger than 22 GeV=c. For B0s !D

,

s a+1 candidates,

only the combination with the largest B0s momentum has been kept.

B0s !D

0_K,+ ; B

0s !D

0_K,a+1

For B0s !D

0_K,+ decays, the B0s momentum had to be larger than 27 GeV=c. Because

of a high combinatorial background for B0s !D

0_K,a+1 decays, the B0s momentum had to

be larger than 29 GeV=c in the D0 ! K+

, channel and larger than 33 GeV=c in the

D0 ! K

+_,+, decay channel. In each event, only the candidate with the largest B0s

momentum was kept. For the K, candidate, identied as \standard", the momentum

had to be larger than 2 GeV=c. The source of the D0 and K, meson pair can be an

excited D meson state. The constraint on the mass value of such a state allows more

soft K, mesons to be considered. The selection on the K, momentum was reduced

to 1.5 GeV=c, if the invariant mass of the D0K, pair was compatible with the mass

of the orbitally excited DsJ(2573) state (the most probable value of J is 2 [25]). One

event was detected, which is compatible with the decay channel B0s ! DsJ(2573)

,+,

DsJ(2573),

! D

0_K,: the momentum of the K, candidate is 1.8 GeV=c and the mass

dierence M(D0K,)

,M(D

0_{) is 716:0}

2:1 MeV=c2. The expected mass dierence of

708:91:8 MeV=c

2 _{is in good agreement with the observed one, taking into account the}

full width of this state which is 15+5

,4 MeV=c

2 _[25].

Main peak

Data set Mass Width () Nsignal Comb. bkg Re ection

(GeV=c2_{) (GeV=c}2_{) % %} Real Data 5:3730:016 0:0290:012 84 2716 -Simulation 5:3700:002 0:0370:002 51 - 73 Satellite peak Real Data 5:0500:054 0:1110:049 158 5513 -Simulation 5:0990:007 0:1480:007 112 - 126

Table 2: Characteristics of the B0s signals and comparison with the simulation. The

expected numbers of events were calculated taking into account the dierent branching fractions as given in Table 1 and the corresponding reconstruction eciencies. These eciencies vary from (0:20:1)% for the B0s !D

0_K,a+1 with D0 !K+ ,+,, up to (10:20:8)% for the B0s ! D , s+ with D, s ! 

,. The tted or expected number of

signal events and the fraction of combinatorial background are given inside a mass window corresponding to 3(2) for the main(satellite) peaks. In real data the number of

events in these mass windows are11(33). TheB0s mass in the simulation is5:370 GeV=c2_.

In the last column the fraction of physical background, discussed in detail in Section 3.3, is given.

The mass spectrum, obtained by summing up the contributions from the dierent channels is shown in Figure 1. The data are indicated by points with error bars and the t result is shown by the solid line. The mass distribution in the signal region was tted

(main narrow peak) and for the presence of partially reconstructed B0s decays (satellite wider peak). According to the expected branching fractions, it was assumed that the dominant contributions for the satellite peak come from the following decay channels:

D, s +, D, s a+1, D (2007)0_K,+, D  (2007)0_K,a+1, D, s + and D,

s +, where the cascade

photon or neutral pion (or both) were not reconstructed. In the simulation, it was veried that the mass distribution of the satellite peak can be described by a Gaussian function as shown in Figure 2. The central values and the widths of the Gaussian functions (main and satellite peaks) in Figure 1 were left free to vary in the t. The combinatorial background was tted using an exponential function with a slope xed according to the simulation. This slope was veried in several ways. Using 2.9 million bb and 5.3 million qq simulated events, the expected mass spectrum was obtained after having removed the

B0ssignal contribution in the mass region of the satellite and main peaks. The sum of the

contributions from b events, charm events and light-quark events is shown in Figure 1 and is in agreement with that obtained in data. Two further checks were performed,

using events selected in the side-bands of the D,

s and D0 candidates and from wrong sign

combinations. The slopes of both distributions are in agreement with those obtained by tting the data and the simulation.

The t to the mass distribution yielded a signal of 84 B0sdecays in the main peak and

158 events in the satellite peak. The probability that the background has uctuated

to give the observed number of events in the main peak is 3  10

,4. Table 2 gives

the characteristics of the observed signals and the comparison with simulation. Specic

decay channels from B0s, B0d, B+ _{and 0b were simulated with statistics ranging from ten}

to several thousand times the expected rates in real data. These samples were used to determine eciencies and re ection probabilities discussed below.

3.3 Re ections from

and

decays

For several B0s decay channels a possible physical background originates from

non-strange B decays, when one of the pions or proton is misidentied as a kaon (kinematic

re ections). The main decay channels are B0d ! D

,+(a+1), D, ! K 0, (which can contribute to B0s ! D , s +(a+1), D, s ! K

0K, candidates) and from B0d

! D

0_,+,

D0 ! K+

, or K+,+, (which can contribute to B0s

! D

0_K,+ candidates). In

the mass region of the main peak, 0:32  0:13 events are expected to originate from

kinematic re ections (with a 19% contribution from 0b decays). These estimates were

obtained using dedicated Monte Carlo samples of B0d and 0b events passed through the

full reconstruction algorithms and satisfying the selection criteria. The corresponding uncertainties come from the limited knowledge of the assumed branching fractions and from the simulated events statistics.

To study the contribution in the satellite peak from kinematic re ections, the same decay processes were considered with channels in which the D meson is accompanied by

a . This gives 1:30:7 events.

In order to look for possible signals coming from kinematic re ections in real data,

B_0s candidates were considered in turn as B_0d or 0b hadrons by changing the kaon into a

pion or an antiproton, respectively. The mass distributions obtained are similar to those

expected from genuine simulated B0s mesons and do not show any accumulation of events

3.4 Reconstruction of non-strange

meson decays

Non-strange B mesons, decaying into a D0 and a small number of pions, were

re-constructed in order to verify the B0s reconstruction algorithms. The B+ ! D

0_+,

B0d!D

(2010),+ and B0d

!D

(2010),a+1 decay channels were studied and their mass

distributions are shown in Figures 3a and 3b. They were tted using a Gaussian func-tion for the signal and using an exponential funcfunc-tion for the combinatorial background. An additional Gaussian function was used in Figure 3a to account for the signal coming

from the following decay channels: B+!D

 (2007)0_+_{, B}+!D 0_{+, B+} !D  (2007)0_+_,

where the 0 _{and/or from the D}

(2007)0 _{and/or  decays were not reconstructed. The}

main selection criteria which were imposed are rather similar to those used in the B_0s

analysis. The information relevant to these reconstructed channels is given in Table 3. The numbers of observed events are in agreement with expectations.

Channel B meson mass Nobs Nexp

(GeV=c2₎ B+!D 0_{+ 5:278} 0:008 245 285 B_0d!D (2010),+ + D(2010),a+1 5:277 0:011 115 104 B0d!D 0_,+ + D0,a+1 5:287 0:024 84 ,

Table 3: Characteristics of the non-strange B decay mode and comparison with the

simulation. The error on the expected number of events comes from the errors in the branching fractions and reconstruction eciencies. The branching fraction of the decay mode in the last row is estimated in this paper.

Finally two B0d decay channels, B0d ! D

0_,+ and B0d

!D

0_,a+1 which are not yet

well established, were considered.

In the strange B sector (Section 3.1) they correspond to the B0s ! D

0_K,+ and

B0s! D

0_K,a+1 decays. B0dmesons were reconstructed using the same selection criteria as

for the corresponding B0s decay channel, but replacing a K meson by a . All particles,

not explicitly identied as protons or kaons were accepted as pions. In order to remove

the B0d!D

(2010),+and B0d

!D

(2010),a+1 contamination, candidates were required

to have a mass dierenceM(D0,)

,M(D

0_{) larger than 0:16 GeV=c2.}

Figure 4 shows the mass distribution for these two decay channels. It was tted with an exponential function for the background and two Gaussian functions for the signals corresponding to the main and satellite peaks, with respective widths equal to about

34 MeV=c2 _{and 60 MeV=c}2_{, as obtained from the simulation. The position of the wider}

Gaussian, corresponding to B0d !D  (2007)0_,+ and B 0d !D  (2007)0_,a+1 signals with

unreconstructed 0 _{or , and the slope of the background exponential function were also}

taken from the simulation. The t to the mass distribution yielded a signal of 84 B0d

decays in the main peak. The probability that the background has uctuated to give the

observed number of events is 310

,2.

The number of observed events in the main peak can be translated into a branching

fraction: Br(B0d !D

0_,+ + D0,a+1) = (3:6

1:9)10

,3: The quoted error is

com-pletely dominated by statistics. The CLEO Collaboration has given an upper limit [25]

only on the decay channel with a pion pair: Br(B0d ! D

0_,+) < 1:6

10

90% C.L.). This limit is consistent with those which can be extracted from the measured channels in this paper:

Br(B0d!D 0_,+) < 1:6 10 ,3 at the 90% C.L. Br(B0d !D 0_,a 1+) < 5:410 ,3 at the 90% C.L.

For this evaluation it was assumed (see Section 3.1) that the decay channel with a+1 is

produced with a rate which is (3:30:9) times larger than the channel with 

+_.

3.5 Study of

oscillations

3.5.1 Algorithm for tagging b or

quark at production time

The signature of the initial production of a b (b) quark in the jet containing the B0s

or B0s candidate was determined using a combination of dierent variables sensitive to

the initial quark state. For each individual variable Xi, the probability density

func-tions fb(Xi) (fb(Xi)) for b (b) quarks were built and the ratio Ri =fb(Xi)=fb(Xi) was

computed. The combined tagging variable is dened as:

xtag = 1,R

1 +R ; where R =

Y

Ri: (11)

The variablextag varies between -1 and 1. Large and positive values ofxtag correspond to

a high probability that the produced quark is a b rather than a b in a given hemisphere. A set of nine discriminant variables has been selected for this analysis. One set (three

variables) is determined in the hemisphere which contains the B0s meson, the other set

(ve variables) in the hemisphere opposite to the B0s meson, and one variable is common

to both hemispheres. Details concerning the denition of these variables and the method are given in reference [10].

An event was classied as a mixed or as an unmixed candidate according to the sign,

QD, of the Ds electric charge for decay channels containing a Ds meson, or according

to the sign of the kaon for D0K,+ decay channels, relative to the sign of the x

tag

variable. Mixed candidates are dened by requiringxtag
QD < 0, and unmixedcandidates

correspond to xtag
QD > 0. The probability, 

tag

b , for tagging correctly the b or b quark,

from the measurement ofxtag, was evaluated by using a dedicated simulated event sample

and was found to be (74.50:5)%.

The corresponding probability for events in the combinatorial background was ob-tained using real data candidates selected in the side-bands of the D signal: the

probabil-ities to classify these events as mixed or unmixed candidates are calledmix_{comb and }unmix_{comb ,}

respectively. For the re ection events the analogous probabilities are called mix_{ref, }unmix_ref

and their values were taken from the simulation.

3.5.2 Proper time resolution

For each event, the B0sproper decay time was obtained from the measured decay length

(LB0

s) and the estimate of the B0s momentum (pB

0

s). The measured position of the D

,

s

or D0 decay vertex, the momentum, and the corresponding measurement errors, were

used to reconstruct a D,

s or a D0 particle. A candidate B0s decay vertex was obtained by

intercepting the trajectory of this particle with the other charged particle tracks which

are supposed to come from the B_0s decay vertex.

For the main peak, the B0s momentum is precisely known since all decay products are

undetected neutral(s) (0_{and/or ) in the B0sdecay. As discussed in Section 3.2, the}

satel-lite peak is assumed to be composed of D,

s +, D, s a+1, D, s +, D, s +and D (2007)0_K,+, D

(2007)0_K,a+1 decays. The rst four decay channels give D,

s+(a+1) and the last two

channels give D0K,+(a+1) nal states. Kinematic mass constrained ts (imposing the

mass of B0s and of the intermediate states with corresponding errors) were performed

assuming always the presence of a coming from the D,

s or D

(2007)0 _{meson decays.}

This is a good approximation also for decay channels containing a+_{meson. These mass}

constrained ts were performed on events lying in the mass region corresponding to 2

of the tted mass of the satellite peak.

Except for the combinatorial background contribution, the predicted proper time dis-tributions were obtained by convoluting the theoretical functions with resolution functions evaluated from simulated events. Due to the dierent decay length resolutions (for the dierent Vertex Detector congurations), proper time resolutions were used for data

sam-ples taken in 1992-1993 and 1994-1995 separately. The proper time resolution,RB

s(t ,ti),

was evaluated from the dierence between the generated time (t) and the reconstructed

time (ti), tting this distribution by the sum of two Gaussian functions:

RB s(t

,ti) = (1,f2)G1(t,ti;1) +f2G2(t,ti;2) (12)

where G1(t, ti;1) and G2(t ,ti;2) are Gaussian functions with the corresponding

resolutions 1 and 2. In the general case, the i resolutions depend on the momentum

uncertainty (see equation (1)). But in this analysis, as the B0s momentum is known

with a good precision, the contribution of the momentum uncertainty to the proper

time resolution is negligible. f2 is the fraction of the second Gaussian function, which, by

convention, is that with the worse resolution. The values of the corresponding parameters, obtained from simulated events, are given in Table 4. The time resolution for events in the satellite peak is only slightly worse than for those belonging to the main peak.

Main peak

Decay channels Years 1(ps) 2(ps) f2

all B0s channels 1992-1993 0.068 0.18 0.27 all B0s channels 1994-1995 0.065 0.12 0.42 Satellite peak D, s +(a+1), D (2007)0_K,+(a+1) 1992-1993 0.066 0.15 0.48 D, s +(a+1), D (2007)0_K,+(a+1) 1994-1995 0.081 0.17 0.30 D, s +, D, s + 1992-1993 0.085 0.21 0.65 D, s +, D, s + 1994-1995 0.092 0.20 0.57

Table 4: Proper time resolution from simulation for 1992-1993 and 1994-1995 data

sets and for the dierent decay channels. It has been parameterised by the sum of two Gaussian functions.

The time distributionPcomb(ti) for the combinatorial background under the main peak

is obtained from real data by tting the time distribution of wrong-sign and right-sign

events lying in the side-bands of the B0s mass distribution. It was veried, in the

simula-tion, that the time distribution for these classes of events is similar to that obtained for

events lying under the B_0s mass peak. The time distribution Pcomb(ti) for the

combina-torial background under the satellite peak was taken directly from the simulation, since

the B momentum for these events. The time distribution ref(ti) for the re ection was

also taken from the simulation.

3.5.3 Fitting procedure

The oscillation analysis is performed in the framework of the amplitude method [13],

which consists in measuring, for each value of the frequency
mB0

s, an amplitudeA and

its error (A). The parameter A is introduced in the time evolution of pure B0s or B0s

states, so that the value A = 1 corresponds to a genuine signal for oscillation. The

time-dependent probability that B0s is detected as a B0s or B0s is then:

P unmix(mix)_{(t) = 1} 2B0 s exp(,t=B 0 s) (1A cos(
mB 0 st)) (13)

where the plus (minus) signs refer to B0s (B0s) decays. The 95% C.L. excluded region for

mB0

s is obtained by evaluating the probability that, in at most 5% of the cases, a real

signal having an amplitude equal to unity would give an observed amplitude smaller than the one measured. This corresponds to the condition:

A(
mB0

s) + 1:645 (A(
mB

0

s)) < 1:

In the amplitude approach, the error(A(
mB0

s)) is related to the probability to exclude

a given value of
mB0

s. The sensitivity is dened as the value of
mB

0

s which would just

be excluded, if the value of A, as measured in the experiment, was zero for all values

of
mB0

s, i.e. it is the expected 95% condence limit that an experiment of the same

statistics and resolution would be expected to achieve (a real experiment would set a

higher or lower limit, because of uctuations in the values of A as a function of
mB0

s).

The probability distributions for mixed and unmixed4 _{events are:}

Pmix_{(ti) =fB}

sP

mix

Bs (ti) +frefP

mix

ref (ti) +fcombPcombmix(ti) (14)

wherefBs, fref andfcomb are the relative fractions of the B0s, re ection and combinatorial

background events, respectively, which satisfy the condition fBs+fref+fcomb=1. The

expressions for the dierent probability densities are:

 B0s mixing probability: P_Bmix s (ti) = f  tag b PBmix s (t) + (1 , tag b )PBunmix s (t) gRB s(t ,ti) (15)

 Re ection mixing probability:

P_refmix_{(ti) =}mix_ref

Pref(ti) (16)

 Combinatorial background mixing probability:

P_combmix_{(ti) =}mix_comb

Pcomb(ti) (17)

The parameters tag_{b ,}mix_{ref and }mix_{comb were dened in Section 3.5.1.}

The amplitude analysis is then performed using all events selected in a mass region

between 4.83 and 5.46 GeV=c2_{. The variation of the background level as a function of}

the reconstructed mass was included in this analysis on an event-by-event basis. Figure 5

shows the variation of the measured amplitude as a function of
mB0

s. With the present

4In the following, only the probability distribution for mixed events is written explicitly; the corresponding probability

level of the statistics, this analysis provides a negligible low limit. On the other hand, its most important feature, despite the low statistics, is the relatively small error on the

amplitude at high values of
mB0

s with respect to the more inclusive analyses. Due to

the limited statistics, the error on A ((A)) can be asymmetric. The error has been

symmetrized by taking the larger value. Figure 6a shows the variation of the measured

error on the amplitude as a function of
mB0

s. In Figure 6b the results from the D



s `[10]

and from the D

s h (see the second part of the current paper) are compared with the

exclusive B0s analysis. It should be noted that, due to the better proper time resolution,

the resolution (A) of the B0s exclusive analysis increases more slowly. The ratio of the

corresponding errors of B_0s exclusive and D

s ` analyses is about 5 (2) at the low (high)

values of
mB0

s.

The behaviour of (A) was investigated using a \toy" Monte Carlo generated with

the same characteristics as those measured in real data. The individual toy experiments

show a similar behaviour of (A), as in the real data, as a function of
mB0

s. For each

value of
mB0

s, the distribution of(A) and its variance was obtained. The central value

and the region corresponding to a 2(A) variation are also shown in Figure 6a.

3.5.4 Study of systematic uncertainties

Systematic uncertainties were evaluated by varying the parameters, which were kept constant in the t according to their measured or expected errors.

 Systematics from the tagging purity:

a variation of 3% on the expected tagging purity for the signal was considered,

following the results given in [10].

 Systematics from the background level and kinematic re ection:

the levels of background and of kinematic re ection were varied separately for the main peak and for the satellite peak according to the statistical uncertainties given in Table 2. Since the level of the combinatorial background was used as a function of the reconstructed mass on an event-by-event basis, the measured central mass

positions and the corresponding widths were also varied by 1 around their tted

values.

 Systematics from the expected resolution on the B decay proper time:

the widths 1 and2 described in Section 3.5.2 and given in Table 4 were varied by

10% [10,27,28].

 Finally, uncertainties in the values of the B0s meson lifetime (B0

s = 1:46

0:06 ps [7])

and in the parameterisation of the proper time of the combinatorial background were taken into account.

In Figure 5, which presents the variation of the measured amplitude as a function of

mB0

s, the shaded area shows the contribution from systematics.

4



s h



analysis with fully reconstructed

Ds

Events with an exclusivelyreconstructed Dsaccompanied by one or more large

momen-tum hadrons were used to perform a second oscillation analysis. This channel is similar

to the D

s` nal state [10] but, instead of a charged lepton, it uses charged hadrons.

It provides a larger number of events but suers from an ambiguity in the choice of the

hadrons and from a reduced B0s purity of the selected sample. This approach has already

4.1 Event selection

The Ds meson is selected in two decay channels:

D, s ! ,;  !K +_K,; D, s !K 0K,; K0 !K+ ,:

Ds candidates were reconstructed by making combinations of three charged particles

located in the same event hemisphere, with a momentum larger than 1 GeV=c and with

reconstructed tracks associated to at least one VD hit. The value of jcos j (see

Sec-tion 3.2) was required to be larger than 0.4 and 0.6 in the D,

s !

, and D,

s !K 0K,

decay channels, respectively. In order to reduce the combinatorial background from char-m and light quarks, the b-tagging probability for the whole event was required to be smaller than 0.5.

In this analysis the neural network algorithm for hadron identication described in

Section 2.3 was used. For the D,

s !

, decay mode, the invariant mass of candidates

was required to be within12 MeV=c

2 _{of the nominal mass and the  momentum was}

required to be larger than 5 GeV=c. If the K+_K, invariant mass was within

4 MeV=c

2

of the nominal mass, both kaon candidates were required to be identied as \very loose"

kaons, otherwise to be identied as \loose" kaons.

For the D,

s ! K

0K, decay mode, the invariant mass of the K0 candidates was

re-quired to be within 60 MeV=c2 of the nominal K

0 mass value and the K0 momentum

was required to exceed 5 GeV=c. The momentum of the K, candidate from D,

s was

re-quired to exceed 3 GeV=c. To suppress the physical background from the D,

!K+ ,,

kinematic re ection, the K,candidate was required to be identied as a \standard" kaon.

For K0

!K+

, decays, \loose" identied K+ were also accepted. In order to suppress

the combinatorial background, the K, candidate was required to be identied as \tight"

kaon, if the invariant mass of the K0 candidates was out of

20 MeV=c

2 _{of the nominal}

K0 mass value, and the value of

jcos j was required to be larger than 0.8.

The selection of a hadron accompanying the Ds candidate is based on an impact

parameter technique. A sample of tracks coming predominantly from B hadron decays was preselected by using their impact parameters and the corresponding errors, both

with respect to the primary vertex (Imp, p) and to the secondary Ds decay vertex

(Ims, s). The hadron was then searched for amongst the preselected particles in the

event, by requiring that its charge was opposite to the Ds charge and that it had the

largest momentum. The eciency of the hadron selection was about 80% and, among

the selected hadrons, (844)% came from a B vertex. Details on the track preselection

as well as on the hadron selection are given in reference [27].

The B decay vertex was reconstructed by tting the selected hadron and the Ds

can-didate to a common vertex. The2_{{probability of the tted B0s vertex has been required}

to be larger than 10,3. In order to increase the resolution on the measured decay length,

only reconstructed events with a decay length error smaller than 0.07 cm were kept. If the previous procedure failed, a new attempt was made, using an inclusive algorithm

which allowed several hadrons to be attached to the Dscandidate. This algorithm is based

on the dierence in the rapidity distributions for particles coming from fragmentation and from B decays. The fragmentation particles, on average, have lower rapidity [29] than B decay products. The charged particles were ordered in increasing values of the

rapidity and were attached in turn to the secondary Ds vertex. Up to three particles

were accepted with their total charge equal to 1 or 0. The rapidity was calculated

as 0:5log ((E + PL)=(E ,PL)), where E is the energy of the particle (assumed to be a

Only particles with a momentum greater than 1 GeV/c were accepted. In addition, for

the tracks satisfying the condition Imp=p < 3, it was required that Ims=s < Imp=p.

Events with a decay length error smaller than 0.07 cm and a 2_{{probability of the tted}

B0s vertex larger than 10,3 were kept.

Ds decay channels Ds signal in 1992-1993 data Ds signal in 1994-1995 data

D, s ! , 322 30 (0:600:04) 46842 (0:530:04) D, s !K 0K, 152 28 (0:700:06) 32435 (0:580:05)

Table 5: Number ofDs mesons reconstructed in the , andK0K, decay channels after

selection of the accompanying hadron(s). The fraction of combinatorial background, given in parentheses, has been evaluated using a mass interval of 2 centred on the tted Ds

mass.

The selected sample, specied as D

sh in the following, contained about 30% of such

\multi-hadron" events. Among them, about 20% have one, 50% two and 30% three se-lected hadrons. The multi-hadron and single-hadron events were treated in a similar way.

Figure 7 shows the Ds signals after selection of the accompanying hadron(s). The mass

distributions were tted with two Gaussian functions of equal widths to account for the

D,

s and D, signals and with an exponential function for the combinatorial background.

All parameters were allowed to vary in the t. Table 5 gives the number of observed

events in the Ds signal, after background subtraction, and the fraction of combinatorial

background. The Ds signal region corresponds to a mass interval of 2 centred on the

tted Ds mass.

The reconstructed number of D,

s ! 

, events using 1994-1995 data is about 1.5

larger than those obtained using 1992-1993 data. This factor re ects the dierence in statistics between the two data sets. Such \statistical scaling" does not apply to the

D,

s ! K

0K, decay mode, where the particle identication, which was better for the

1994-1995 data set (see Section 2), plays a more important role.

Four events are in common with the exclusively reconstructed B0s sample: one event

in the main peak and three in the satellite peak. These events were removed from the

D

s h sample for the oscillation analysis.

4.2 Sample composition

The D

sh sample contained a large physical background due to D

s from non-strange

B hadron decays and from cc fragmentation. Four sources of events, originating from B

decays, were considered: two from B_0s and two from non-B_0s mesons, namely, B decaying

to one or two charmed mesons comprising at least one Ds. The relative fractions of these

sources were calculated using ve input parameters:

 Br(b !D  s X) at LEP [30];  Br(b !D  s X) at (4S) [31];  Br(b !B0s) at LEP [25];

 the probability in the non-strange B meson, that a D

,

s is produced at the lower

vertex: Br(Bu;d !D

,

s X) [32];

 the probability to have two charmed hadrons in a b-decay: Br(b!DDX) [33].

The last two probabilities were assumed to be the same for all B species. To estimate